My wife used my credit card in her business and used 20,000 (AMEX CARD) and then she couldn’t pay off the debt. Now it’s hurting my credit and we wanted to move the debt from me to her. Taking into consideration that I admit that I allowed her to use the card and she admit that she used it on her business.
According to here, some credit cards allow you to transfer balances between authorized users/joint account holders. However, American Express is not one of them.
You could try transferring the balance to a credit card that does; preferably one that gives you a 0% interest rate on balance transfers for 12 to 18 months.
In the UK there are a couple of credit cards available which offer a 0% rate on money transfers. Other cards also allow money transfers, however tend to charge a punitive rate of interest so I wouldn't suggest considering those as serious options. Your wife could take out a 0% money transfer credit card (if there's one available in your country), use a money transfer to get cash out of the card into her bank account, and then give you the money to pay off your cards. The end result being the debt transferred to a card in your wife's name. As with all credit cards, the actual amount you will be able to do this with will depend on a number of factors